'test-score-based' originates from modern English compounding of the nouns 'test' and 'score' combined with the past-participle adjective 'based' (from 'base'), where 'test' referred to an examination or trial, 'score' referred to a numerical result or tally, and 'base' (via Latin/Greek roots) meant a foundation.

'test-score-based' is a recent formation in English formed by compounding; 'test' (sense 'examination') developed into modern English usage in the 19th–20th centuries, 'score' (sense 'number of points') developed from earlier senses of 'mark' or 'tally,' and 'base' comes from Latin/Greek 'basis' via Old French/Latin, yielding the adjective 'based' used to mean 'having X as a foundation.' Together these elements produced the modern compound adjective.

Initially the separate elements meant 'trial/examination' ('test'), 'tally/point total' ('score'), and 'foundation' ('base'); over time they combined in modern English to form the compound meaning 'having a foundation in test scores' (i.e., 'determined by test scores').